Find its displacement?

Question

A spring with natural length 0.5 m has length 50.5 cm with a mass of 2 gm suspended from it. The mass is initially displaced 1.5 cm below equilibrium and released with zero velocity. Find its displacement for t>0.

 

The equation of motion is y"+(k/m)y=0. How do I figure out m? I know that k should be 32.

Answer 1

Yang,

 

What does k represent here? If you are using SI units, the mass should be in grams, right? The length in meters, and the time in seconds.

 

The stretched length is .505 m. Using Hooke's Law, it is stretched an additional .005 m = .5 cm when the mass is attached, so:

 

F = kx  ⇒  ma = kx  ⇒  2(9.8) = k(.005)  ⇒  k = 9800.

 

I may not be understanding your problem, but m usually represents the mass in a problem like this. The k used in the last equation is the spring constant.

 

You need to be more specific because different textbooks/authors/teachers use different variables for these quantities.

 

Please let me know if this makes any sense to you and if you need to clarify.